A Pipe open at one end has length 0.8 m. At the open end of the tube… | MHT CET 2026 (15 Apr, Shift 1)

Q25MHT CET 2026 · 15 APR · SHIFT 1Difficult

Organ Pipes & Resonance Tube

A Pipe open at one end has length $0.8$ m. At the open end of the tube a string $0.5$ m long is vibrating in its first overtone and resonates with fundamental frequency of pipe. If tension in the string is $50$ N, the mass of string is (Neglect end correction) (Speed of sound $= 320$ m/s)

Show answer and solution

Answer: (c)

Pipe (closed at one end) fundamental: $f = \frac{v}{4L} = \frac{320}{4 \times 0.8} = 100\text{ Hz}$
String first overtone (2nd harmonic): $f = \frac{2}{2l}\sqrt{\frac{T}{\mu}} = \frac{1}{0.5}\sqrt{\frac{50}{\mu}}$
$2\sqrt{\frac{50}{\mu}} = 100 \Rightarrow \mu = \frac{50}{2500} = 0.02\text{ kg/m}$
Mass $= \mu l = 0.02 \times 0.5 = 0.01\text{ kg} = 10\text{ g}$
So the answer is (c) 10 gram.

Report a mistake

More questions on Organ Pipes & Resonance Tube

In a pipe closed at one end, air column is vibrating in its second overtone. The column…MHT CET 2025 (22 Apr, Shift 2)
In an open end organ pipe of length ' L ', if the velocity of sound is ' V ', then the…MHT CET 2025 (25 Apr, Shift 2)
The fundamental frequency of an air column in a pipe closed at one end is 150 Hz. If the…MHT CET 2025 (26 Apr, Shift 2)
The fundamental frequencies of vibrations of air column in pipe open at both ends and in…MHT CET 2025 (25 Apr, Shift 2)
An organ pipe has fundamental frequency 80 Hz. If its one end is closed, the frequencies…MHT CET 2025 (22 Apr, Shift 1)
A pipe open at both ends produces a fundamental frequency n₁. When the pipe is kept with…MHT CET 2025 (23 Apr, Shift 1)
A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped…NEET 2025
In an experiment with a closed organ pipe, it is filled with water by (1/5) th of its…JEE Main 2025 (4 Apr, Shift 1)

Organ Pipes & Resonance Tube question from MHT CET 2026 (15 Apr, Shift 1)

More questions on Organ Pipes & Resonance Tube